i think you need to use the Lambert W-function here: Lambert W-Function -- from Wolfram MathWorld
Hello,
I am having an exponential equation that depends on 3 different variables, which are included in the constants a, b and c....
solving this equation, I get something of the form of ln(a + bx) - cx = 0
I don't manage to simplify the equation any further
I was wondering whether this is actually possible without any numerical method, I would like to get an equation for x as a function of a, b and c (or actually some other constants that form a, b and c).
Or is there maybe any approximations method , such as a Taylor development or something, which gives me a solution with a certain accuracy?
Would be nice if someone could help me!
Cheers
i think you need to use the Lambert W-function here: Lambert W-Function -- from Wolfram MathWorld
Thank you very much for your answer!
I had already heard about the Lambert W-function in order to solve problems like this, but I have to admit that I don't really understand how that works... (I'm not tha good in maths, I'm just a chemist )
I understood what the Lambert function is but I don't manage to apply it to solve my problem :S
Could you help me, please?
Thanks a lot
Dude forget that Lambert W(hatever) stuff.
Here goes:
First plot the functions g(x)=ln(a+bx) and h(x)=cx, both in the same coordinate plane. Abscissas of the intersection points are solutions to the equation g(x)=h(x) or ln(a+bx)=cx. Now from that picture you can estimate the intervals that contain the solutions. Say that interval is I=[u,v].
Now you just have state the precision you need (epsilon=0.00005 would mean 4 significant decimal digits) and use an iterative method that would find the solution in the interval I=[u,v]. Good choice of method would be Newton tangent method, or even plain bisection method provided you don't need great precision.